~~$17\%$ a$\_(1),$a$\_(0),$b$\_(1),$b$\_(0).$

a$\_(1)$a$\_(0)$ and b$\_(1)$b$\_(0)$ represent two $2-$bit unsigned binary integers

Three outputs, c$\_($out$),$s$\_(1)$ and s$\_(0).$

c$\_($out $)$ represents a carry signal from the sum of the two $2-$bit integers and

s$\_(1)$s$\_(0)$ represents the $2-$bit unsigned binary sum of the two $2-$bit integers.

For credit, ensure you order your input a$\_(1)$a$\_(0)$b$\_(1)$b$\_(0)$ and

Your output c$\_($out $)$s$\_(1)$s$\_(0).$

Notice there is no c$\_($in$).$ You're welcome! Why is this a very good thing from your point of view?

$(1\mathrm{.}0$ Points$)$ For each of the following two expressions, select all of the following definitions $[$i$,$ ii$,$ iii, iv$]$ which apply.

$(1\mathrm{.}0$ points$)$

i$.$ Product term

ii$.$ SoP expression

$($a$)$ ab$^(\text{'})$cd$^(\text{'})$

$($b$)$ a$^(\text{'})+$b$+$c$^(\text{'})+$d

iii. Sum term

iv$.$ PoS expression

Answ

Answ

Using properties $1$ to $10,$ reduce the following expressions to a minimum SOP form. Show each step;

the numbers of terms and literals in minimum form are shown in parentheses. $(1\mathrm{.}0$ points$)$

$($a$)$ x$^(\text{'})$y$^(\text{'})$z$+$x$^(\text{'})$yz$+$xy$^(\text{'})$z$^(\text{'})+$xyz$^(\text{'})(2$ terms, $4$ literals$)($b$)$ w$^(\text{'})$x$^(\text{'})$y$^(\text{'})$z$+$wx$^(\text{'})$y$^(\text{'})$z$+$wx$^(\text{'})$yz$+$wxyz $(2$ terms, $6$ literals$)$

$($c$)$ w$^(\text{'})$x$^(\text{'})$y$^(\text{'})$z$^(\text{'})+$w$^(\text{'})$x$^(\text{'})$yz$^(\text{'})+$w$^(\text{'})$x$^(\text{'})$yz$+$wxy$^(\text{'})$z$^(\text{'})+$wxyz$^(\text{'})+$wxyz $(4$ terms, $12$ literals$)$ Show a block diagram of a system using AND, OR$,$ and NOT gates to implement the following functions.

Your AND and OR gates have a fan$-$in of two $(2).$ Assume that variables are available only uncomple$-$

mented $($this means NOT gates are required when variables are complemented$).$ Do not manipulate

the equation. $(1\mathrm{.}0$ points$)$

wxy$^(\text{'})$z$^(\text{'})+$vy$($w$+$x$)^(\text{'})+$w$^(\text{'})$y

Translate the following circuit into an algebraic expression, then put it in sum of product form. Write

your final answer as f$($w$,$x$,$y$,$z$)=$dots $(1\mathrm{.}0$ points$)$

Answe

AnsweGiven the following function h$,$ find the complement, h$^(\text{'}).$ Only single variables may be complemented

in the answer. $(1\mathrm{.}0$ points$)$

h$=$ab$^(\text{'})$c$+$a$^(\text{'})$bc$^(\text{'})+$d$($c$^(\text{'})+$a$^(\text{'}))($b$^(\text{'})+$a$^(\text{'}))$

For each of the following functions:

f$($a$,$b$,$c$,$d$)=\backslash$Sigma m$(1,6,9,11,15)$

g$($a$,$b$,$c$,$d$)=\backslash$Sigma m$(0,6,7,8,14)$

$($a$)$ Provide truth table for both f and g behavior.

$($b$)$ Convert to an algebraic expression in sum of minterms form.

$(1\mathrm{.}0$ Points$)$

PLEASE PLEASE PLEASEEE ANSWER ALL QUESTIONS COMPLETELY WITH ALL DETAILS PLEASE